Currently, digital transmission technology has been moving to the transmission of higher and higher data rates over given channel bandwidths, using multilevel signaling and faster bit rates.
In digital transmission, a plurality of pulses are transmitted in specific time slots and thereafter are received at corresponding time slots by a receiver. As bit rates increase, there can be a considerable spillover of pulse energy into adjacent time slots, resulting in intersymbol interference.
For example, a transmitter may transmit a stream of pulses at T-second intervals. Inherent characteristics of the transmission system causes these pulses to spread out as they traverse the system. Therefore, the receiver might receive the pulses that have overlapped into adjacent time slots. At the receiver, the original pulse message may be derived by sampling at the center of each time slot. The receiver then bases a decision on the amplitude of the signal measured at that point and assigns a 1 or 0 based on the decision.
If, however, the pulses have overlapped sufficiently in adjacent time slots, the receiver may mistake an intended 0 as 1, due to intersymbol interface.
Intersymbol interference may be minimized by purposely widening the transmission bandwidth as much as desired. However, virtually all transmissions are bound by bandwidth efficiency. Furthermore, widening bandwidths may result in allowing too much noise to interfere in the system. Therefore, signal waveshapes and consequently filters are purposely designed to eliminate interference with as small a transmission bandwidth as possible.
One signal waveshape producing zero intersymbol interference is ##EQU1## pulse as shown in FIG. 1. The main lobe (center portion) of the spectrum is generally all that is needed to ensure accurate information transfer.
The waveform illustrated in FIG. 1 goes through zero at equally spaced intervals, multiples of T seconds away from the peak at the origin. The waveform of FIG. 1 is the impulse response of an ideal low-pass filter illustrated in FIG. 2. The frequency spectrum of an ideal filter is flat, over frequency to a cut-off frequency fc hertz and is zero elsewhere, 2fc pulses may thus be transmitted over a bandwidth of fc hertz if the waveshape of FIG. 1 is used.
Therefore, by shaping pulses into the waveform of FIG. 1, it is possible to eliminate intersymbol interference. A major difficulty with such a waveshaping is that ideal low-pass filters are presently unavailable.
Alternatively, it has been found by H. Nyquist that some other classes of waveshapes may also provide zero intersymbol interference. This particular class of waveshapes are designed such that their frequency characteristic has odd symmetry about the low-pass cut-off point. Filters with such odd symmetry characteristics are commonly known as Nyquist filters.
Currently, various filtering techniques have been implemented. One approach is a strictly digital filter using digital signal processing techniques. Another approach is using arbitrary waveform generators. Still another technique is designing analog filters.
Digital signal processing is now considered to be well established, and is suited to the general problem of digital data spectral filtering. A finite impulse response (FIR) filter would be a good implementation as it can possess linear phase response, adequate spectral roll-off and perfect repeatability. One difficulty with digital signal processing (DSP) technique is its limited application to high-bit transmission rates like those required by video data transmission. A typical compressed video transmission rate can be in the order of 3.MB/sec (million bits per second). This is an order of magnitude faster than what can be handled using available digital signal processing (DSP) hardware. To achieve high transmission rates there is need to resort to full custom GaAs IC development, which is not cost efficient.
An alternate digital approach is to develop a type of arbitrary waveform generator. This involves using a digital look-up table to program the output of a digital-to-analog converter (DAC) to a specific level depending on the past and current serial data values, simulating an ideally filtered signal. This technique, however, requires a very high clock rate. Implementing the filter would require some very high speed digital circuits, drawing and dissipating more power than desired.
Analog filters can be scaled for high frequency applications and are comparatively easy to implement. However, a problem with analog filters is that they generally do not exhibit linear phase response, which is a requirement for eliminating intersymbol interference. One approach to linearize phase responses is designing phase compensation networks. For video data transmission such analog filters with phase compensation networks become complicated. Additionally, their characteristics are not consistent without extremely low tolerance and high cost parts.
Another approach is known as programmable transversal filter (BTF). Typically, the digital data stream is shifted into a shift register. The parallel output taps of the shift register are then summed using stored coefficients or weights to result in an analog output. The output is then smoothed through anti-aliasing filter.
One difficulty with the filter is the delay associated with retrieving the stored coefficient from memory. Another difficulty with the filter is determining the tap weights in the system. The weights associated with the taps of the filter are derived from the impulse response to the desired filter. Given the desired frequency domain response of the filter, the impulse response can be calculated by an inverse Laplace transformation. For a Nyquist filter, the mathematics involved in the inverse transformation can be very complicated and intractable. Thus, there is a need for a simplified design of a Nyquist filter suitable for very high speed digital transmissions.